Pewne problemy kształtowania powłok osiowo-symetrycznych w stanie błonowym

The paper deals with the optimal design of axially symmetrical shells in membrane state loaded by general system of loadings represented by body forces (own weight, rotation) and by external loading – pressure. As a criterion of design the minimal volume of the shell has been assumed. The problem has been formulated as a classical problem of calculus of variations. The possible solution shave to be found in the class of uniform strength shells. Two basic types of strength conditions have been disinguished: ,,condition of the uniform strength in narrower sense'' (1.1) and the more general one ,,condition of the uniform strength in broader'' (1.2). With the aid of the HMH conditions (broader sense) the shape of the optimal shells under different system of loadings have been given. The question, if the shell of uniform strength in narrower sense is optimal one has been examined. In order to answer this we looked for external loading which transforms the shell satisfying the Euler-Lagrange equations into the shell of the uniform strength in narrower sense (1.1). It turns out that such a shell does not satisfy all demanded conditions of optimality.